Technical Field
The present disclosure relates to a magnetic sensor including a Lorentz force transducer, which is driven at a frequency different from its natural resonance frequency. Furthermore, the present disclosure relates to a method for driving a Lorentz force transducer.
Description of the Related Art
As is known, today available are the so-called magnetic sensors based upon the Lorentz force, which are also known as Lorentz force magnetometers and exploit, precisely, the Lorentz force to obtain measurements of magnetic field, as described, for example, in U.S. Pat. No. 7,642,692.
Lorentz force magnetometers represent a valid alternative, for example, to Hall sensors and to the so-called anisotropic magnetoresistive (AMR) sensors. In particular, Lorentz force magnetometers are suited to form single-chip triaxial sensors; moreover, these magnetometers can be integrated with gyroscopes, so as to form sensors with nine axes. However, Lorentz force magnetometers feature non-negligible levels of consumption, as well as not particularly wide bandwidths.
In general, the principle of operation of a magnetometer based upon the Lorentz force is exemplified in FIG. 1, where a magnetometer of this type is in fact shown, designated as a whole by 1, and referred to in what follows for brevity as “magnetometer 1”.
The magnetometer 1 comprises a transducer 2, which is of the MEMS (microelectromechanical systems) type and in turn comprises a stator 3 and a rotor 4. The stator 3 comprises a first fixed electrode 6 and a second fixed electrode 8, made of semiconductor material.
The first fixed electrode 6 comprises a first fixed-electrode subregion 7a and a second fixed-electrode subregion 7b, which are electrically connected to one another and are fixed with respect to a substrate (not shown), which is made, for example, of semiconductor material.
The second fixed electrode 8 comprises a third fixed-electrode subregion 9a and a fourth fixed-electrode subregion 9b, which are electrically connected to one another, are electrically separated from the first and second fixed-electrode subregions 7a, 7b and are fixed with respect to the substrate.
The substrate mechanically carries the first, second, third, and fourth fixed-electrode subregions 7a-7b, 9a-9b. 
The rotor 4 comprises a first suspended element 12 and a second suspended element 14, which are physically suspended, at a distance, over the substrate. The first and second suspended elements 12, 14 have shapes, for example, of parallelepipeds with a length equal to L, measured along the axis y of an orthogonal reference system xyz. Furthermore, the first and second suspended elements 12, 14 are arranged so as to be parallel to one another and aligned along the axis x.
The first and second suspended elements 12, 14 may be made, for example, of semiconductor material. In addition, each of the first and second suspended elements 12, 14 has a first end and a second end opposite to one another, which are fixed, respectively, to a first anchorage element 16 and a second anchorage element 18, which are in turn fixed with respect to the substrate. The first and second anchorage elements 16, 18 are made of semiconductor material.
The rotor 4 further comprises a third suspended element 20, which is made, for example, of semiconductor material and comprises a first suspended-element subregion 22 and a second suspended-element subregion 24, which are fixed with respect to one another.
The first suspended-element subregion 22 has an elongated shape, extends along the axis x and is provided with a first end and a second end, which are opposite to one another and are constrained, respectively, to the first and second suspended elements 12, 14. In particular, the first end of the first suspended-element subregion 22 is fixed to a central portion of the first suspended element 12, whereas the second end of the first suspended-element subregion 22 is fixed to a central portion of the second suspended element 14. Furthermore, the first suspended-element subregion 22 extends between the first fixed-electrode subregion 7a and the third fixed-electrode subregion 9a, on one side, and the second and fourth fixed-electrode subregions 7b, 9b, on the other.
The second suspended-element subregion 24 includes a first cantilever element 30 and a second cantilever element 32, each of which has an elongated shape, for example parallelepipedal. Furthermore, each of the first and second cantilever elements 30, 32 has a respective first end and a respective second end, opposite to one another; the first end is fixed to a central portion of the first suspended-element subregion 22, whereas the second end is free.
In detail, the first and second cantilever elements 30, 32 extend parallel to the axis y, hence parallel to the first and second suspended elements 12, 14, and are moreover arranged specularly with respect to the first suspended-element subregion 22. Furthermore, the first cantilever element 30 is arranged, at a distance, between the first and third fixed-electrode subregions 7a, 9a, whereas the second cantilever element 32 is arranged, at a distance, between the second and fourth fixed-electrode subregions 7b, 9b. 
In greater detail, in the magnetometer 1, the first and second cantilever elements 30, 32 form a single piece with the first suspended-element subregion 22. Furthermore, the first, second, and third suspended elements 12, 14, 20 form a single piece.
For practical purposes, the first and second fixed-electrode subregions 7a, 7b form a first plate of a first capacitor C1, the second plate of which is formed by the first and second cantilever elements 30, 32. Furthermore, the third and fourth fixed-electrode subregions 9a, 9b form a first plate of a second capacitor C2, the second plate of which is formed once again by the first and second cantilever elements 30, 32.
The magnetometer 1 further comprises a transduction circuit 35 and a current generator 40.
The transduction circuit 35 is electrically connected to the first plates of the first and second capacitors C1, C2, as well as to the second (shared) plate of the second cantilever element 30.
The current generator 40 is electrically coupled to the transducer 2. In particular, the current generator 40 is electrically coupled to the first and second anchorage elements 16, 18 and is such as to generate, in use, a current i(t).
The current i(t) flows in part in the first suspended element 12 and in part in the second suspended element 14, without traversing, to a first approximation, the first suspended-element subregion 22, since the ends of this latter are at one and the same potential. More in particular, in each of the first and second suspended elements 12, 14 there flows substantially half of the current i(t). Consequently, in the presence of a magnetic field directed, for example, parallel to the axis z, each of the first and second suspended elements 12, 14 is subject to a Lorentz force FL(t), the modulus of which isFL(t)=½·i(t)·L·B where B is the modulus of the magnetic induction.
Under the action of the Lorentz force FL(t), each of the first and second suspended elements 12, 14 undergoes elastic deformation in such a way that its own central portion translates parallel to the axis x.
The first and second suspended elements 12, 14 hence function as springs, the deformation of which entails a translation of the third suspended element 20 parallel to the axis x, the extent and direction of said translation being, respectively, proportional to the modulus and direction of the magnetic induction B. For instance, with reference once again to FIG. 1, in the presence of a magnetic field, the translation of the third suspended element 20 is such that the first and second cantilever elements 30, 32 move away, respectively, from the first and second fixed-electrode subregions 7a, 7b and approach, respectively, the third and fourth fixed-electrode subregions 9a, 9b. 
In detail, assuming that, in the absence of magnetic field, i.e., in resting conditions, the third suspended element 20 is arranged in such a way that the first and second capacitors C1, C2 have one and the same capacitance C0, in the presence of the magnetic induction B illustrated in FIG. 1, it is found that to a first approximation the first capacitor C1 assumes a value of capacitance equal to C0−ΔC, whereas the second capacitor C2 assumes a value of capacitance equal to C0+ΔC.
The transduction circuit 35 is designed to generate an electrical signal proportional to ΔC, which is hence proportional to the modulus of the magnetic induction B and moreover indicates the direction of the latter. This electrical signal is also known as “measurement signal”.
In greater detail, if we designate by x0 the distance that separates, in resting conditions, one between the first and third fixed-electrode subregions 7a, 9a from the first cantilever element 30 (this distance being equal to the distance between one between the second and fourth fixed-electrode subregions 7b, 9b and the second cantilever element 32), we have that the sensitivity of the magnetometer 1 is, at a low frequency,
                    Δ        ⁢                                  ⁢        C                    Δ        ⁢                                  ⁢        B              ⁢          (      t      )        =                              C          0                          x          0                    ·                                    F            L                    ⁡                      (            t            )                                    B          ·          k                      =                            C          0                          x          0                    ·              L        k            ·              i        ⁡                  (          t          )                    where k is the elastic stiffness of the deformable body formed by the first, second, and third suspended elements 12, 14, 20, i.e., the constant that links a force to which the deformable body is subject to the corresponding translation of its centroid with respect to the resting conditions. The elastic stiffness k is a function of the elastic stiffnesses of the first and second springs 12, 14.
This having been said, today two different techniques are known for driving Lorentz force magnetometers, these techniques being described in what follows once again with reference to the magnetometer 1 illustrated in FIG. 1.
According to a first driving technique, the current generator 40 operates in d.c., in such a way that the relation i(t)=IC applies. This driving technique is simple to implement; however, it entails that the magnetometer 1, when driven in this way, has a somewhat reduced sensitivity; moreover, the magnetometer 1 operates in a region where the electronic noise is rather high. To overcome at least in part this problem, it is possible to increase the value of the current IC, with consequent increase in consumption, and/or to increase the surfaces of the plates of the first and second capacitors C1, C2, with consequent increase in the area of semiconductor material occupied by the magnetometer 1.
Furthermore, the first driving technique entails that the magnetometer 1 is sensitive also to external vibrations and accelerations.
According to a second driving technique, instead, the current generator 40 operates in a.c., and in particular operates in such a way that the current i(t) has a periodic waveform, for example of a sinusoidal or square-wave type, at a frequency fi equal to the resonance frequency f0 of the transducer 2.
In greater detail, the transducer 2 is characterized by a respective transfer function Hm(f), also known as frequency response, which sets in relation, as the frequency varies, the values of amplitude, in sinusoidal regime, of the Lorentz force FL(f), to which each of the first and second suspended elements 12, 14 is subject, with the corresponding values of amplitude of the translation X(f) of each of the first and second suspended elements 12, 14 with respect to the corresponding resting position, i.e., the position assumed in the absence of magnetic field. In particular, the transfer function is equal to the ratio X(f)/FL(f).
FIG. 2 shows an example of the transfer function Hm(f), which has a peak at a value of frequency equal, precisely, to the aforementioned resonance frequency f0.
This having been said, the resonance frequency f0 is not exactly known beforehand, in the sense that, even though it is possible to estimate, based on the characteristics of design of the transducer 2, a nominal resonance frequency fN, i.e., an estimate of the resonance frequency f0, this nominal resonance frequency fN does not coincide perfectly with the resonance frequency f0. Furthermore, over time, the resonance frequency f0 may vary, for example on account of temperature variations. Consequently, in order to guarantee that the frequency fi of the current i(t) is effectively equal to the resonance frequency f0, the current generator 40 is controlled in closed-loop fashion in such a way that the frequency f1 of the current i(t) follows the resonance frequency f0.
The second driving technique enables to obtain a sensitivity that is higher than that obtained by the first driving technique. However, the implementation of a closed-loop control, which is based upon generation of an oscillating signal with an amplitude that varies together with the amplitude of the magnetic field, entails an increase in the circuit complexity. In addition, high sensitivity and resolution may be obtained at the expense of bandwidth. In this connection, in fact, it should be noted how the impact of Brownian noise on the performance of the transducer 2, when the latter is driven with the second driving technique, is directly proportional to the damping coefficient of the peak of the transfer function Hm(f). Consequently, by reducing the damping coefficient, the effects of the noise are reduced, and hence the resolution increases; this means that the peak narrows and hence the sensitivity increases, given that the latter may be expressed as:
            Δ      ⁢                          ⁢      C              Δ      ⁢                          ⁢      B        =                              C          0                          x          0                    ·                        F          L                          B          ·          k                      =                            C          0                          x          0                    ·              L        k            ·                                i          ⁡                      (            t            )                                      ·      Q      where Q is the quality factor of the peak of the transfer function Hm(f). However, the fact that the peak narrows moreover means that the bandwidth is reduced, since the latter is approximately equal, in this driving conditions, to f0/(2Q). For these reasons, generally the bandwidths of magnetometers driven with the second driving technique are in the region of a few hertz.
Moreover, the adoption of the second driving technique entails that the current generator 40 and the corresponding closed-loop control cannot be used for supplying further transducers additional to the transducer 2, for example integrated in a single chip together with the transducer 2 to form a multiaxial magnetic sensor. In fact, each of these further transducers has a respective resonance frequency, which is inevitably different from the resonance frequency f0 of the transducer 2. Consequently, each of the further transducers is coupled to a respective current generator, controlled in closed-loop fashion in such a way that the frequency of the current generated thereby will follow the resonance frequency of the further transducer. Consequently, the current used by a triaxial magnetic sensor is three times the current used by a uniaxial magnetic sensor.